geerky42
  • geerky42
Does Batman Equation really work? And can we "union" relations? (Sorry for long reply.)
Mathematics
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schrodinger
  • schrodinger
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geerky42
  • geerky42
I just happened to discover this question in Math Stack Exchange (MSE): http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real/54568#54568 Here's the image: |dw:1435886055793:dw| http://i.stack.imgur.com/VYKfg.jpg I tried to graph it on Desmos: https://www.desmos.com/calculator/cscx2zcrlf Graphing each factor separately turns out well, however when I multiply all factors, graph won't appear. I think Desmos just choke on it, so I tried something simple; https://www.desmos.com/calculator/enxuzekis6 Yet it doesn't show anything... So apparently image above is not true. My questions are: \(\Large 1)\) Is there any way to union relations? By "union," I mean in \(\mathbb R^2\), if you union \(f(x,y)=0\) and \(g(x,y)=0\), then you would have new union relation \(U(x,y)=0\), which if you graph it, then \(f(x,y)=0\) and \(g(x,y)=0\) would both be graphed simultaneously. From image, it's \(U(x,y) = f(x,y)g(x,y)=0\), but it seems that it is not true. \(\Large 2)\) Why does no one seem to notice that image is not true in MSE question?
anonymous
  • anonymous
A relation is a set, so obviously you could union two relations.
geerky42
  • geerky42
Yeah I know. Not sure what's correct word for that, but let's just stick with "union" By "union," I mean saying if you graph \(f(x,y)=0\) and \(g(x,y)=0\), you would see something on xy plane. If we "union" these relations, then we would have new relation \(U(x,y)=0\), such that if you graph \(U(x,y)\), then you would see same thing as if you graph \(f(x,y)=0\) and \(g(x,y)=0\) separately at the same time.

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geerky42
  • geerky42
From shown image, you just multiply relations, but to me, it doesn't work.
just_one_last_goodbye
  • just_one_last_goodbye
In my opinion it doesn't work :/ very complex and in testing ur not going to really make a perfect batman sign on the graph xD
anonymous
  • anonymous
We are such math nerds XD
geerky42
  • geerky42
For example; saying we have \(f(x,y) = x^2+y^2 -1= 0\) and \(g(x,y) = (x+2)^2+y^2-1=0\) Then \(U(x,y)\) would graph this:|dw:1435887037303:dw| Exactly what is \(U(x,y)\)? and how can I "combine" f(x,y) and g(x,y) to form U(x,y)?
geerky42
  • geerky42
Wut now it works. https://www.desmos.com/calculator/uezz1quzdy Now I am confused lol...
geerky42
  • geerky42
Got something to do with restrictions, I guess. That circles equation above here has no restriction, but Batman Equation does.
geerky42
  • geerky42
https://www.desmos.com/calculator/enxuzekis6 First relation is restricted to \(x>1\) Second relation is restricted to \(x<1\) So together they would not appear in graph simply because they would be somewhere in complex. Just like Batman Equation. Is there any way to prevent that? OK I think that's too much to ask lol...
geerky42
  • geerky42
@iambatman ( ͡° ͜ʖ ͡°)
anonymous
  • anonymous
Im batman (in husky batman voice) o.o
anonymous
  • anonymous
Yes, the roots of \(f\cdot g\) is the union of the roots of \(g\) and the roots of \(f\).
anonymous
  • anonymous
Only exceptions are when you have different domains
anonymous
  • anonymous
You intersect the domains, then you union the roots in that intersected domain
geerky42
  • geerky42
OK, I think I asked rather silly and pointless question. But thanks for put in effort for me.
nincompoop
  • nincompoop
Superman > Batman
Australopithecus
  • Australopithecus
nincompoop I am afraid you made a mistake, it should be: Superman < Batman
UsukiDoll
  • UsukiDoll
That's super cool. I wonder if there will be a bunch of equations that can produce the Avengers Logo? When I was taking Calculus III there were some equations in polar coordinates that produced flowers, the number 8, or the infinity symbol.
UsukiDoll
  • UsukiDoll
Anyway, graphing these equations separately was a good idea. If it was bunched up together, wouldn't something overlap and eventually the Batman Logo will no longer appear?
TheSmartOne
  • TheSmartOne
@iambatman should know xD
anonymous
  • anonymous
Haha, I believe it was here I posted something similar long time ago, in any case it seems you've figured out what your problem was? @geerky42 @nincompoop I resent that!
ybarrap
  • ybarrap
FYI - Here is the Batman Equation implemented in Geogebra: \( \href{http:///www.geogebra.org/m/114}{Batman}\)

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